Category: Relation and Functions

Question Number 67187 by mathmax by abdo last updated on 23/Aug/19 $$letf\left(x\right)=arctan\left(x^3\right)$$$$1)calculate{f}^{\left(n\right)}\left(x\right)and{f}^{\left(n\right)}\left(0\right)$$$$2)developpfatintegrserie$$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{\mathrm{3}} \right){dx} \…

Question Number 67055 by Tony Lin last updated on 22/Aug/19 $$let{\mathbb{Z}}_{+}=\mathbb{N}\cup \left\{0\right\},f:{\mathbb{Z}}_{+}\times {\mathbb{Z}}_{+}\to {\mathbb{Z}}_{+}$$$$f(m,n)=\frac{(m+n)(m+n+1)}{2}+m$$$$provethatfisaone-to-onefunction$$$$andalsoanontofunction$$ Terms of Service…

Question Number 67034 by mathmax by abdo last updated on 22/Aug/19 $$calculate\sum _{n=1}^{\mathrm{\infty }}\frac{cos\left(2nx\right)}{n}$$ Commented by mathmax by abdo last updated on 23/Aug/19…

Question Number 67023 by mathmax by abdo last updated on 21/Aug/19 $$findthesequence{U}_{n}wichverify{U}_n+U_{n+1}=sin\left(n\right)\mathrm{\forall }nfromn$$ Commented by mathmax by abdo last updated on…

Question Number 67015 by mathmax by abdo last updated on 21/Aug/19 $$letf\left(x\right)=arctan(1+e^{-\sqrt{1+x^2}})$$$$calculate{f}^{{}^{\prime }}\left(x\right)and{f}^{{}^{″}}\left(x\right).$$$$1)find{lim}_{x\to +\mathrm{\infty }}f\left(x\right)and{lim}_{x\to -\mathrm{\infty }}f\left(x\right)$$$$\left.\mathrm{3}\right){study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \…